# which of the following boolean algebra expression is incorrect?

#### oslon

Joined Oct 18, 2023
9

I can only solve the first one which is correct, all others seem incorrect to me.

#### Irving

Joined Jan 30, 2016
3,859
I think A & D are correct and B & C are wrong.

#### WBahn

Joined Mar 31, 2012
30,008
View attachment 315371
I can only solve the first one which is correct, all others seem incorrect to me.
Why do they seem incorrect to you?

Since there are only four variables, a truth table would only have sixteen rows. So it's a fairly simply matter to establish whether the relationships are true or not. Once you have done that, then you can also let them guide you toward figuring out how to perform the Boolean algebraic manipulations to establish the same thing.

Also, to prove that one of them is incorrect, it is sufficient to show a single, specific set of values for each variable that fails the claimed equality. So look first for the low hanging fruit. If one side has (something)A, then you know that this is FALSE if A is FALSE, regardless of what the something is. So look on the other side and see if you can set A to FALSE and then find values for the other variables that makes the result TRUE.

To gain insight, you can also exploit symmetries. For instance, in (C), on the left hand side there is no distinction between A and B, but on the right hand side, A and B are treated very differently. This is a red flag, so you might want to consider a case that leverages that apparent disparity.

Are these single-answer or multiple-answer problems (i.e., there supposed to be a single correct choice, or can there be multiple correct choices)?